Use the given information to find the minimum sample size required to estimate an unknown population mean.how many weeks of data must be randomly sample to estimate the mean weekly sales of a new line of athletic footwear? We want a 99% confidence that the sample mean is within $200 of the population mean, and the sample standard deviation is known to be $1100.
To find the minimum sample size required to estimate an unknown population mean, we can use the formula:
n = [(Z * σ) / E]^2
where:
n = sample size
Z = Z-score, corresponding to the level of confidence
σ = population standard deviation
E = maximum error (margin of error)
Given:
Confidence level: 99% (which corresponds to a Z-score of 2
To find the minimum sample size required to estimate an unknown population mean, we can use the formula:
n = [(Z * σ) / E]^2
where:
n = sample size
Z = Z-score, corresponding to the level of confidence
σ = population standard deviation
E = maximum error (margin of error)
Given:
Confidence level: 99% (which corresponds to a Z-score of 2.58 for a two-tailed test)
Maximum error: $200
Population standard deviation: $1100
Plugging in the values into the formula, we have:
n = [(2.58 * $1100) / $200]^2
n = [2838 / $200]^2
n = (14.19)^2
n ≈ 201.64
Therefore, the minimum sample size required to estimate the mean weekly sales of the new line of athletic footwear is approximately 202 weeks of data.
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